## SciPost Submission Page

# On four-point connectivities in the critical 2d Potts model

### by Marco Picco, Sylvain Ribault, Raoul Santachiara

### Submission summary

As Contributors: | Sylvain Ribault |

Arxiv Link: | https://arxiv.org/abs/1906.02566v1 |

Date submitted: | 2019-06-25 |

Submitted by: | Ribault, Sylvain |

Submitted to: | SciPost Physics |

Domain(s): | Theor. & Comp. |

Subject area: | High-Energy Physics - Theory |

### Abstract

We perform Monte-Carlo computations of four-point cluster connectivities in the critical 2d Potts model, for numbers of states $Q\in (0,4)$ that are not necessarily integer. We compare these connectivities to four-point functions in a CFT that interpolates between D-series minimal models. We find that 3 combinations of the 4 independent connectivities agree with CFT four-point functions, down to the $2$ to $4$ significant digits of our Monte-Carlo computations. However, we argue that the agreement is exact only in the special cases $Q=0, 3, 4$. We conjecture that the Potts model can be analytically continued to a double cover of the half-plane $\{\Re c <13\}$, where $c$ is the central charge of the Virasoro symmetry algebra.